Searching for Universality of Turbulence in the Earth's Magnetosphere

Turbulence in space plasmas remains a fundamental challenge, and Earth's magnetosphere (MSP) offers a natural laboratory for its study. Using high-resolution magnetic field data from the Magnetospheric Multiscale (MMS) mission, we extend a stochastic Markovian framework to analyze turbulence across 10 diverse magnetospheric regions, including key reconnection sites. We show that magnetic field fluctuations are well described as Markov processes in scale across the kinetic domain. Multi-scale conditional Probability Density Functions (PDFs) reveal Markovian properties beyond the Einstein-Markov scale. The Kramers-Moyal coefficients display linear and quadratic dependencies, and the Fokker-Planck equation accurately reproduces empirical conditional PDFs, with stationary solutions matching observed Kappa distributions. Scale invariance, characterized by power-law behavior and self-similar PDFs, holds up to $\sim 0.4$ s in most regions but breaks in day-side reconnection jets. These findings support the universality of the Markovian cascade description across the magnetosphere, while identifying region-specific deviations that reflect differing energy dissipation mechanisms.